Wednesday, March 24, 2010

Manifold

“…the Lorenz manifold is giving you information about what is happening anywhere in state space […]. What’s fascinating about this – because we are not supposed to be able to predict when we go left or right in the Lorenz system – is that there must be something very complicated about this surface that makes it impossible to say whether we are on the left or the right side of it. It turns out that’s because the Lorenz manifold rolls up in a very intricate way. You can imagine this a bit as if you were folding and rolling up a sheet of fabric over and over again, and then picking a point somewhere inside. Now you have to decide: is this point on the left or the right side of the sheet? It’s very hard to tell.”